Formula for Calculating Percent

Calculate ratios, increases, and portions with precision

1. Find a Percentage of a Value

Example: What is 15% of 200?

of

2. Find the Percentage of One Number to Another

Example: 40 is what percentage of 200?

is what % of

3. Percentage Increase or Decrease

Example: Change from 50 to 75.

to

Understanding the Formula for Calculating Percent

A percentage represents a fraction of 100. It is a dimensionless ratio used to express how large or small one quantity is relative to another. Whether you are calculating a grade, a discount, or a scientific variance, the underlying logic remains consistent.

The Basic Percentage Formula

The core formula for calculating percent is:

Percentage = (Part / Whole) × 100

Calculating Percentage Change

To find the percentage increase or decrease between two values, use the following steps:

1. Subtract the original value from the new value.
2. Divide that result by the absolute value of the original value.
3. Multiply by 100 to get the percentage change.

% Change = [(New Value – Initial Value) / Initial Value] × 100

Practical Examples

• Test Scores: If you score 45 out of 50, your percentage is (45 / 50) × 100 = 90%.
• Population Growth: If a town's population grows from 1,000 to 1,200, the increase is ((1200 – 1000) / 1000) × 100 = 20%.
• Discounts: If an item is 25% off a $80 price, the discount value is (25 / 100) × 80 = $20.

function calculateScenario1() { var p = parseFloat(document.getElementById("perc1_p").value); var v = parseFloat(document.getElementById("perc1_v").value); var res = document.getElementById("res1"); if (isNaN(p) || isNaN(v)) { res.innerHTML = "Please enter valid numbers."; res.style.color = "#e74c3c"; return; } var result = (p / 100) * v; res.innerHTML = "Result: " + result.toLocaleString(undefined, {maximumFractionDigits: 4}); res.style.color = "#27ae60"; } function calculateScenario2() { var v1 = parseFloat(document.getElementById("perc2_v1").value); var v2 = parseFloat(document.getElementById("perc2_v2").value); var res = document.getElementById("res2"); if (isNaN(v1) || isNaN(v2) || v2 === 0) { res.innerHTML = v2 === 0 ? "Cannot divide by zero." : "Please enter valid numbers."; res.style.color = "#e74c3c"; return; } var result = (v1 / v2) * 100; res.innerHTML = "Result: " + result.toLocaleString(undefined, {maximumFractionDigits: 4}) + "%"; res.style.color = "#27ae60"; } function calculateScenario3() { var v1 = parseFloat(document.getElementById("perc3_v1").value); var v2 = parseFloat(document.getElementById("perc3_v2").value); var res = document.getElementById("res3"); if (isNaN(v1) || isNaN(v2) || v1 === 0) { res.innerHTML = v1 === 0 ? "Initial value cannot be zero." : "Please enter valid numbers."; res.style.color = "#e74c3c"; return; } var diff = v2 – v1; var result = (diff / Math.abs(v1)) * 100; var type = result >= 0 ? "Increase" : "Decrease"; res.innerHTML = type + ": " + Math.abs(result).toLocaleString(undefined, {maximumFractionDigits: 4}) + "%"; res.style.color = result >= 0 ? "#27ae60" : "#e67e22"; }